Seismic data obtained in field surveys are typically recorded using a common midpoint (CMP) field technique as shown in FIG. 1. Acoustic energy in the form of a wave train is introduced into the earth from a series of “shot” sources S which are spaced apart from a common midpoint (CMP). Energy from each of the sources S strikes a common subsurface reflection point (CRP) and a portion of that energy is returned to a series of spaced apart receivers R. Using this acquisition technique, gathers of traces are recorded which are characterized by increasing shot to receiver offset distance and a common known surface (CMP) or common subsurface reflection point (CRP). These gathers of traces contain recordings of desirable signals that have been reflected from the common reflection point (CRP) of the subsurface at various reflection angles θr and/or refracted from subsurface formations. Further, the recorded traces also include other unwanted components, i.e. noise, in addition to the desired signals.
A reflection coefficient is a measure of the ratio of reflected wave to incident wave amplitudes, indicating how much energy is reflected from a subsurface interface. Reflection coefficients are a function of a subsurface formation's elastic properties, including changes at interfaces in compressional wave velocity, shear velocity and density. In reflection seismic art, the earth's reflection coefficients are recovered below a common known surface location from the recorded seismic amplitude response or seismic traces. The actual seismic disturbance from a single reflecting interface is characterized by a time varying response or wavelet that is related to the earth's overburden properties as well as to the reflection seismic acquisition equipment.
A wavelet is a one-dimensional pulse characterized by amplitude, frequency, and phase. The wavelet originates as a packet of energy from a source S, having a specific origin in time, and is returned to receivers R as a series of events or reflected wavelets distributed in time and energy. This distribution is dependent upon velocity and density in the subsurface and the relative position of the sources S and receivers R.
The field recorded traces of a CMP gather are typically subjected to a number of steps in a processing sequence to separate the desired signals from noise, to reduce the effect of time and offset varying wavelets and to align and compare amplitude responses from common interfaces. An important step in trace alignment is to apply normal moveout removal NMOR to the data either directly in an NMOR application or indirectly through a prestack imaging step. Travel times to common subsurface interfaces for differing shot to group offsets are calculated using the CMP gather acquisition geometry and estimates of the subsurface propagation velocity of seismic energy traveling from the shot location to a common subsurface reflection point (CRP) and then back to a receiver location. The differences in travel time between zero and non-zero shot to receiver offsets are used to map the amplitudes of traces from field record time coordinates to zero offset time coordinates. After application of NMOR whether directly applied to CMP gather traces or indirectly applied within a prestack migration to generate CRP gather traces, amplitudes of signal traces in the gather can then be (1) summed together to form stacked traces; (2) compared to one another within an amplitude versus offset (AVO) analysis; or (3) inverted for amplitude attributes from which detailed interface properties are to be deduced from changes in amplitude response.
FIGS. 2A-C illustrate the effect of wavelets and normal moveout removal (NMOR) on a single time-offset CMP gather made up of identical, equal amplitude reflections from a layered earth model composed of randomly spaced subsurface interfaces. FIG. 2A shows a CMP gather of interface reflection coefficients (RC series) illustrating the moveout effect (time convergence) of reflections from different interfaces. FIG. 2B depicts the same CMP gather with each reflection coefficient replaced by a wavelet whose amplitude is proportional to the reflection coefficient. Offset varying interference effects are shown in the form of offset varying amplitudes for a common event. FIG. 2C presents the data of FIG. 2B after application of NMOR demonstrating that moveout has generated offset varying wavelets which result in offset varying amplitudes for the equal reflection coefficients. Note in FIG. 2C that there are changes in reflection amplitude and bandwidth which are due to pre-NMOR wavelet interference as well as to NMOR correction. As a result, amplitudes in traces from different offsets differ from one another even when the underlying reflection coefficients are equal. Therefore, these NMOR corrected amplitudes are not considered to be of “true relative amplitude”.
Especially because of ongoing deep water exploration and development efforts, AVO analysis and inversion are now being applied to CRP trace gathers containing processed seismic amplitudes that have been reflected from subsurface interfaces at reflection angles from 0° to 60° or more. As shown by FIG. 3 depicting the amplitude spectrum of a single event reflected from an interface at angle θr, application of NMOR will map the amplitude spectrum and phase spectrum of a seismic wavelet to frequencies equal to cos θr times the original pre-NMOR frequency while also amplifying the amplitude spectrum of the data by a factor of (cos θr)−1 relative to the zero angle reflected event. Accordingly, for a 60° reflected event, NMOR will shift an 40 Hz amplitude response to 20 Hz while doubling the strength of the amplitude spectrum. Wavelets have both an amplitude spectrum and a phase spectrum. For the purposes of this specification, here after the term “spectra” refers to both of the amplitude spectrum and phase spectrum of a wavelet.
When multiple reflection events are present, NMOR stretches the interfering event response differently at each offset resulting in a more complex offset dependent interference as shown in FIG. 2C. Such NMOR stretch effects make it difficult to directly compare common event amplitude strengths from different offset traces to one another. Another complexity is that even after extensive processing, traces in a CMP gather will typically have embedded wavelets which vary with both time and offset. These wavelet variations are due to remaining acquisition and propagation effects and to NMOR stretch effects. Velocity analysis, which is required to align events between near and far offsets, also becomes problematic when amplitude responses for a common event vary significantly from near to far offsets. Moreover, at high frequencies NMOR stretch will reduce the signal-to-noise ratio improvements normally expected as a result of stacking seismic traces together.
U.S. Pat. No. 5,684,754 to Byun et. al teaches a method for removal of NMOR stretch from CMP gather traces. This method relies on prior knowledge of an embedded wavelet and the measurement of a NMOR stretch factor from a semblance analysis of seismic data. This technique does not provide a true relative amplitude compensation of NMOR induced amplitude effects and is thus is less than desirable for AVO analysis.
Swan, H. W., 1997, “Removal of Offset-Dependent Tuning in AVO Analysis”, Expanded Abstracts of 67th Annual, Int. SEG Mtg., pp. 175-178, teaches a method for reduction of NMOR stretch effects from AVO attributes (eg. AVO intercepts and gradients) that are computed from NMOR processed traces that are not compensated for NMOR stretch effects. As a result, this method has the shortcoming of not being applicable for the correction of CMP or CRP gather traces.
U.S. Pat. No. 6,516,275 to Lazaratos describes removing wavelet stretch effects from seismic traces prior to operations such as stacking or computing AVO attributes. A method for destretching individual traces is taught in which time and offset varying filters are used to match the response of stretched, nonzero offset traces to that of a zero offset (and destretched) trace. Because this method involves making each nonzero offset trace match a zero offset trace by designing and applying an equalization filter, the method can alter relative amplitude relationships between traces when reflectivity strength varies. This method fails to restore trace amplitudes to the relative values consistent with each traces' reflectivity being convolved with a pre-NMOR wavelet. To be true amplitude this method must assume that all pre-NMOR traces have the same wavelets as the zero offset pre-NMOR trace. Moreover, this method also implicitly assumes that the reflectivity of each trace averaged in time has the same value at all offsets as it does on the zero offset trace—an assumption that is generally not met across a wide range of offsets or reflection angles.
Accordingly, there is a need for a method and apparatus which overcome shortcomings of previous methods and apparatus which fail to destretch seismic traces so as to recover true relative amplitudes of seismic reflections between traces of differing offsets. More particularly, these methods fail to compensate for offset varying reflection interference effects due to normal moveout. The present invention provides a solution to these shortcomings.